SLAC Magnetic Measurements Date: 04-22-1998 Time: 14:25:00 Project: PEP2INT Magnet Type: QUAD Magnet Name (Serial #): Q1L Measurement System: 2895 Operator: zw Run Number: 4 Comment: q1cin = 0 deg, q1cout = -20 deg Temperature Measurements Table Top Thermistor, T = 21.91577 deg C Magnet Thermistor # 1, T = 21.98532 deg C Magnet Thermistor # 2, T = 22.07526 deg C Harmonics Measurements Date: 04-22-1998 Time: 14:53:06 Magnet Name: Q1L Run Number: 4 FIELD HARMONICS Harmonics at Rcoil = .045002 m Main Harmonic N = 2 n BLn sigBLn THspole sigTH BLn/BLN sBLn/BLN (Tm) (Tm) (deg) (deg) (%) (%) --- ------------+------------ --------+-------- ---------+--------- 1 0.260066E+00 0.859787E-05 -90.81 0.00 43.09722 0.00193 2 0.603441E+00 0.181275E-04 -46.51 0.00 100.00000 0.00425 3 0.143616E-03 0.403385E-06 -37.26 0.01 0.02380 0.00007 4 0.963435E-04 0.667957E-07 10.33 0.03 0.01597 0.00001 5 0.175733E-03 0.170978E-06 -19.18 0.02 0.02912 0.00003 6 0.113728E-03 0.214049E-06 -16.05 0.01 0.01885 0.00004 7 0.204753E-04 0.249784E-06 -16.06 0.08 0.00339 0.00004 8 0.175344E-04 0.321779E-06 14.61 0.10 0.00291 0.00005 9 0.373570E-04 0.131617E-06 -10.90 0.06 0.00619 0.00002 10 0.121626E-04 0.112092E-06 -0.64 0.23 0.00202 0.00002 11 0.531021E-05 0.309044E-06 0.67 0.30 0.00088 0.00005 12 0.964285E-05 0.208446E-06 -1.18 0.12 0.00160 0.00003 13 0.903801E-05 0.199817E-06 -12.06 0.18 0.00150 0.00003 14 0.119468E-04 0.583778E-06 -7.80 0.12 0.00198 0.00010 15 0.534037E-05 0.291554E-06 -6.40 0.08 0.00088 0.00005 16 0.867509E-05 0.308492E-06 2.94 0.09 0.00144 0.00005 17 0.189458E-04 0.224598E-06 -6.56 0.09 0.00314 0.00004 18 0.506785E-04 0.358004E-06 3.62 0.02 0.00840 0.00006 19 0.163822E-04 0.256771E-06 -5.32 0.04 0.00271 0.00004 20 0.391465E-04 0.518557E-06 5.90 0.03 0.00649 0.00009 21 0.176613E-04 0.363628E-06 2.49 0.05 0.00293 0.00006 22 0.298273E-04 0.747518E-06 7.93 0.06 0.00494 0.00012 23 0.242747E-04 0.176196E-06 -4.00 0.04 0.00402 0.00003 24 0.390752E-05 0.530698E-06 -4.38 0.36 0.00065 0.00009 25 0.113380E-04 0.424118E-06 -5.25 0.05 0.00188 0.00007 26 0.273510E-04 0.610988E-06 2.43 0.04 0.00453 0.00010 27 0.102215E-04 0.536900E-06 1.93 0.04 0.00169 0.00009 28 0.433728E-05 0.194116E-06 -6.42 0.16 0.00072 0.00003 29 0.102249E-04 0.362472E-06 2.90 0.10 0.00169 0.00006 30 0.135955E-04 0.427731E-06 -4.05 0.04 0.00225 0.00007 31 0.323659E-05 0.293817E-06 -2.02 0.08 0.00054 0.00005 32 0.335901E-05 0.400926E-06 -1.93 0.19 0.00056 0.00007 33 0.368674E-05 0.297400E-06 -5.44 1.37 0.00061 0.00005 34 0.395286E-05 0.151523E-06 -4.58 0.12 0.00066 0.00003 35 0.224054E-05 0.384335E-06 0.28 0.53 0.00037 0.00006 36 0.334868E-05 0.205356E-06 -1.17 2.07 0.00055 0.00003 37 0.445464E-05 0.431184E-06 1.69 0.11 0.00074 0.00007 38 0.133532E-05 0.595739E-06 4.54 0.90 0.00022 0.00010 39 0.379414E-05 0.312058E-06 -1.33 9.23 0.00063 0.00005 40 0.228016E-05 0.617635E-06 1.30 1.56 0.00038 0.00010 The magnetic center is at X = -19392.6 +- 0.9 microns Y = -275.9 +- 1.4 microns View from the top of the magnet: y ^ | S N --> x N S Temperature Measurements Table Top Thermistor, T = 22.03317 deg C Magnet Thermistor # 1, T = 22.02084 deg C Magnet Thermistor # 2, T = 22.11197 deg C SUMMARY OF THE CALCULATIONS AND CONVENTIONS USED Field expansion (Bryant, CERN 92-05, p. 55) Br = Sum Bref (r / rref)^n-1 [-an cos(n th) + bn sin(n th)] Bt = Sum Bref (r / rref)^n-1 [ an sin(n th) + bn cos(n th)] For flux calculations, we re-express Bt Bt = - Sum Brefn (r / rref)^n-1 sin[n (th - THspole)] Flux from the origin to a wire bundle of N turns at R Flux = Int_0^R Bt L N dr = - Sum Brefn L N rref (1 / n) (R / rref)^n sin[n (th - THspole)] Fluxn = - Brefn L N rref (1 / n) (R / rref)^n sin[n (th - THspole)] Integrator output The integrated coil voltage VT is sampled and Fourier analyzed The FFT gives VTn and PhiVTn in the formula VTn(i) = VTn cos(n 2pi i / N + PhiVTn), VT(i) = Sum(VTn(i)) VTn(th) = VTn cos(n th + PhiVTn) Equating the flux to the integrator output gives Brefn L N rref (1 / n) (R / rref)^n = VTn BLn|_rref = n VTn / (N rref (R / rref)^n) <<<--- -sin[n (th - THspole)] = cos(n th + PhiVTn) = -sin(n th + PhiVTn - pi / 2) - n THspole = PhiVTn - pi / 2 THspole = - (PhiVTn - pi / 2) / n <<<--- For our planar bucking coil, we have: Nm turns at Rm (main winding) Nd turns at Rd and -Rd (dipole bucking) Nq turns at Rq and -Rq (quadrupole bucking) various return windings at R = 0 The sin[n (th - THspole)] dependence must be included for -R. At -R, sin[n (th + pi - THspole)] = cos(n pi) sin[n (th - THspole)] = (-1)^n sin[n (th - THspole)]. VTn = BLn|_rref rref (1 / n) { Nm (Rm / rref)^n - Nd (Rd / rref)^n + Nd (-Rd / rref)^n - Nq (Rq / rref)^n - Nq (-Rq / rref)^n } Set rref = Rm, take out Nm VTn = BLn|_Rm Rm (1 / n) Nm { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n } BLn|_Rm = n VTn / (Rm Nm) { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n }^(-1) Define BFn = { 1 + (-1 + (-1)^n) (Nd / Nm) (Rd / Rm)^n + (-1 - (-1)^n) (Nq / Nm) (Rq / Rm)^n } BLn|_Rm = n VTn / (Rm Nm BFn) THspole = - (PhiVTn - pi / 2) / n Harmonic Strength Ratios: The main field, denoted by capital N, is the field harmonic with the largest strength at the coil radius. The field strength ratio is defined by Rn = BLn / BLN It gives the ratio of each harmonic field strength to the main field strength at the coil radius. Calculation Of The Magnetic Center: In the quadrupole's frame, Bx' = G * y', By' = G * x'. In the coil's frame (unprimed frame) the magnetic center is at (x0, y0). In the coil's frame, Bx = G * (y - y0), By = G * (x - x0). This gives the magnetic center in terms of the measured dipole field. x0 = - By / G, y0 = - Bx / G In terms of the measured integrated strengths, Xcenter = - (1/GL) * BL1 * sin(THspole1) Ycenter = - (1/GL) * BL1 * cos(THspole1)